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Simplifying x(12 + -2x)(10 + -2x) = 0 Multiply (12 + -2x) * (10 + -2x) x(12(10 + -2x) + -2x * (10 + -2x)) = 0 x((10 * 12 + -2x * 12) + -2x * (10 + -2x)) = 0 x((120 + -24x) + -2x * (10 + -2x)) = 0 x(120 + -24x + (10 * -2x + -2x * -2x)) = 0 x(120 + -24x + (-20x + 4x2)) = 0 Combine like terms: -24x + -20x = -44x x(120 + -44x + 4x2) = 0 (120 * x + -44x * x + 4x2 * x) = 0 (120x + -44x2 + 4x3) = 0 Solving 120x + -44x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(30 + -11x + x2) = 0 Factor a trinomial. 4x((5 + -1x)(6 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {0, 5, 6}
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